Problem: The product of a number $M$ and six less than $M$ is $-5$. What is the sum of all possible values of $M$?
Solution: Converting the given information to equational form, we find $M(M-6) = -5$.  Rearranging, $M^2 - 6M + 5 = 0$.  Using Vieta's equations for sum and product of roots, we find that the sum of the solutions to this equations is $-(-6) = \boxed{6}$.